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Mining Maximal Induced Bicliques using Odd Cycle Transversals [article]

Kyle Kloster, Blair D. Sullivan, Andrew van der Poel
2019 arXiv   pre-print
Specifically, the runtime is parameterized by the size k of an odd cycle transversal (OCT), a vertex set whose deletion results in a bipartite graph.  ...  The best known algorithm in general graphs is due to Dias et al., and runs in time O(M |V|^4 ), where M is the number of maximal induced bicliques (MIBs) in the graph.  ...  Conclusions We present a new algorithm OCT-MIB for enumerating maximal induced bicliques in general graphs, with runtime parameterized by the size of an odd cycle transver-sal.  ... 
arXiv:1810.11421v2 fatcat:vjvsxeghm5bc7gfy3rlip4trvy

Faster Biclique Mining in Near-Bipartite Graphs [article]

Blair D. Sullivan, Andrew van der Poel, Trey Woodlief
2019 arXiv   pre-print
Many applications focus on the enumeration of all maximal bicliques (MBs), though sometimes the stricter variant of maximal induced bicliques (MIBs) is of interest.  ...  Recent work of Kloster et al. introduced a MIB-enumeration approach designed for "near-bipartite" graphs, where the runtime is parameterized by the size k of an odd cycle transversal (OCT), a vertex set  ...  an odd cycle transversal (OCT set): a set of nodes O such that G[V \ O] is bipartite.  ... 
arXiv:1903.01538v1 fatcat:r3h25ruh5jalxb72k7bjwfvchm

Minimal matrices in the Bruhat order for symmetric (0,1)-matrices

Henrique F. da Cruz, Rosário Fernandes, Susana Furtado
2017 Linear Algebra and its Applications  
Our final words of thanks go to all of you who are gathered here with us on our tiny Island, and we wish you an enjoyable and successful conference here in Qawra, St Paul's Bay.  ...  A biclique is a maximal bipartite complete induced subgraph of G. The biclique graph of a graph G, denoted by KB(G), is the intersection graph of all bicliques of G.  ...  Tardos, Maximizing the spread of influence through a social network, Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining (2003) 137-146. [2] P.  ... 
doi:10.1016/j.laa.2017.05.014 fatcat:zlcp5rb2sjeqvlyaajvf2nyoby

Ordered Sets for Data Analysis [article]

Sergei O. Kuznetsov
2019 arXiv   pre-print
., are illustrated with applications in particular subject domains, from chemoinformatics to text mining and natural language processing.  ...  In the bipartite graph (G ∪ M, I) of the context a concept corresponds to an inclusionmaximal complete bipartite subgraphs (maximal bicliques), also not necessarily maximum. Example 5.1.  ...  Prove that in an arbitrary graph the number of vertices with odd degree is even.  ... 
arXiv:1908.11341v1 fatcat:qusrwndmvrby3hz66clcs2diwa

A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Compiled by

Thomas Zaslavsky
1996 unpublished
Fouquet 1997a On the optimal transversals of the odd cycles. Discrete Math. 169 (1997), 169-175. MR 1449714 (98c:05094) (GN: incid) 1967a Programme, Spiele, Transportnetze. B.G.  ...  Problem 1: Is there an odd hole on a particular vertex? Problem 2: Is there an odd induced path joining two specified vertices?  ...  To decide whether a specified arc of a digraph lies in an even cycle, or in an odd cycle, are NP-complete problems (Prop. 2.1) .  ... 

Putting Data on the Map (Dagstuhl Seminar 12261)

Katarzyna Wac, David Hausheer, Markus Fiedler, Paolo Bonato, Michael Fellows, Jiong Guo, Dániel Marx, Saket, Stephen Kobourov, Alexander Wolff, Frank Van, Ham
2012 unpublished
We showed that using approaches similar to the one for LinearArrangement [1], one can obtain efficient algorithms for all three problems on balanced bounded-degree trees.  ...  Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like Odd Cycle Transversal, Chordal Deletion, Planarization, η-Transversal, Long  ...  Equivalently, the question is if there is a subset S of size at most k that intersects every odd cycle in G.  ... 

JA4AI-Judgment Aggregation for Artificial Intelligence(Dagstuhl Seminar 14202) The Future of Refactoring (Dagstuhl Seminar 14211) Geometric Modeling (Dagstuhl Seminar 14221)

Kira Adaricheva, Giuseppe Italiano, Hans Büning, György, Franz Dietrich, Ulle Endriss, Davide Grossi, Gabriella Pigozzi, Marija, Danny Dig, William Griswold, Emerson Murphy-Hill (+5 others)
2014 unpublished
The algorithm is based on covering bipartite graphs with bicliques.  ...  Refactoring is a technique for supporting this highly dynamic software life cycle.  ...  For odd degree, the common and the spherical Bézier representation by Alfeld et al. have a simple geometric relationship.  ...